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# Mock Exam Q7

Posted by ian.coetzer
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 Mock Exam Q7 November 11, 2008 11:31AM Registered: 13 years ago Posts: 137 Rating: 0
Hi, please comment on my solution,
the image is quite large you may have to click on it so that it can download in a seperate browser window/tab only then does it enlarge it and make it more readable

 Re: Mock Exam Q7 November 11, 2008 11:32AM Registered: 13 years ago Posts: 137 Rating: 0
Here is the url, it does not seem to allow you to click on it

Proposed Solution - Link to Larger Image
 Re: Mock Exam Q7 November 11, 2008 12:22PM Registered: 13 years ago Posts: 137 Rating: 0
Here is my proposed answers for 7b to 7d, i cannot figure out the answer for 7e

Once again here is the link as well because it is so small below

 Re: Mock Exam Q7 November 11, 2008 12:44PM Registered: 14 years ago Posts: 45 Rating: 0
Hi I wrote the below mail to the lecturer about 7f (only notice now that there is a numbering problem so actualy e)

Mock exam question 7 f
As there are no sentence supplied for this question. Will it be correct to state that the sentences must be converted to CNF and that the Resolution algorithm must be applied to proof that alpha implies beta. Should a description be given of the algorithm.

CNF and the resolution algorithm should work. Sometime a simple truth table also does the job. No, you do not need to describe the algorithm unless it is explicitly asked.
 Re: Mock Exam Q7 November 11, 2008 01:01PM Registered: 13 years ago Posts: 137 Rating: 0
Ok, when I draw a truth table it is only true if:
alpha = true
beta = false
now what now? what conclusion should one derive from this?

thanks

oh, and by the way what did you think of all my other proposed answers?
7a) to 7d)?
 Re: Mock Exam Q7 November 11, 2008 01:34PM Registered: 14 years ago Posts: 45 Rating: 0
I have not done "a" yet.

7c is valid see p210 Valid sentences are also known as tautologies and P V notP is valid or a tautology same if you draw a truth table for p -> p.

What worries me about e is that for alpha to entail beta, (alpha^not beta) must be unsatisfiable. On p211 it states that a sentence is satisfiable if it is true in some model which is the case in the truth table that you drew up. They way I see the question is that I was not supplied with "real" sentences for alpha and beta as per p215-216 as a result I can not prove it so kept my answer general.

Henk
 Re: Mock Exam Q7 November 11, 2008 01:41PM Registered: 13 years ago Posts: 137 Rating: 0
Aaa, ok my mistake!!!

7.c) is VALID since it does lead to a tautology ! ! !

if it was P and notP then it is a whole different story though.
 Re: Mock Exam Q7 November 11, 2008 01:44PM Registered: 14 years ago Posts: 45 Rating: 0
100% correct.
 Re: Mock Exam Q7 November 11, 2008 03:55PM Registered: 13 years ago Posts: 526 Rating: 0
Hey Ian

I might be wrong, but I got a slightly different answer for (a):
(-P \/ -Q \/ R) /\ (-P \/ Q) /\ P /\ -R

Additionally, what happen when we apply resolution laws to this?
I get Q/\-Q, which is invalid.
 Re: Mock Exam Q7 November 11, 2008 06:43PM Registered: 13 years ago Posts: 137 Rating: 0
*** NEWSFLASH ***

SanozOr you are ... CORRECT ! ! ! !

Please find below the correction, at first I did not think that I was wrong so I did not try and simplify the sentence and just went for it and came to the same result as you proposed in the above post!!! so shocked in getting it wrong myself initially here is the correction ! ! !

Link to correction of proposed answer ...

 Re: Mock Exam Q7 November 12, 2008 10:38AM Registered: 14 years ago Posts: 78 Rating: 0
What did you use to draw those pretty symbols ?
 Re: Mock Exam Q7 November 12, 2008 11:02AM Registered: 11 years ago Posts: 343 Rating: 0
you guys rock.
 Re: Mock Exam Q7 November 12, 2008 11:19AM Registered: 11 years ago Posts: 343 Rating: 0
f:

From the truth table you have drawn, we can conclude that A only entails B when (A & ! is NOT true, as A entails B means that wherever A is true, B should be true, and this is not satisfied by A&!B.
If we draw the column for !(A&!, we see that the scenario where A is true and B is false is excluded so A will entail B.
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